You might want to change your location in your profile... it makes you difficult to take seriously
I speak from experience when I say that it is very difficult to prove that your parents did this to you and to sue them for it. You can likely get proof that you were beaten into deafness but, if you are an adult (which it very much looks like you are), you will probably have a very hard time finding any kind of proof of this happening that would stand up in court. You would need witnesses other than your father and some kind of evidence to back up your story. Evidence from the doctor would be extremely helpful but, at least in the US, the law is not on your side especially since you say this happened a long time ago. The law does not care if your father cried or if he is a coward-- it cares about the hard facts.
Your best bet is to, of course, still try to get legal help. Definitely consult with several lawyers before settling on one and let them know of your financial situation up front so that you don't waste each other's time.
Think about this realistically, though: you've waited a long time and the statute of limitations for abuse is horrifyingly short. I was outside of it by 2 months with my police report and only got a snide "why did you wait so long" in reply. You also have circumstantial evidence that may or may not be able to be backed by medical evidence. So you will have to prepare yourself to possibly not get anything out of this at all. And the lawyers you speak to will be thinking that exact same thing too.
You
definitely need to seek counselling for this. A lot of children are beaten and abused and nothing is done about it. If your father is still in your life you might want to think about how damaging that could be to your psyche. Try out different therapists until you find one whom you like. Getting a second or third or fourth opinion before settling on your therapist is very important. If you do not like your therapist you won't get very far with him or her. Make sure that you feel comfortable enough to open up to this person or at least to the idea of opening up to them in the future once trust has been established.
Good luck,
Soul